Lord Peter Ricketts’ comments come after thousands of people gathered outside Downing Street on Monday to protest against the US President receiving a state visit.
More than 1.6 million people have also signed a government petition calling for the visit to be cancelled.
Public outrage has been building since Friday when Trump made an executive order banning refugees from seven Muslim-majority countries from entering the US.
May has faced growing pressure to cancel the visit, but Downing Street has stood by the decision, saying on Monday that the invitation had been “extended and accepted”.
Lord Ricketts, who was permanent secretary at the Foreign Office between 2006 and 2010, criticised the timing of Trump’s invitation.
He pointed out that previous presidents would normally be in office for about three years before receiving a British state visit.
Speaking to BBC Radio 4’s Today programme on Tuesday, Lord Ricketts said: “Of course I agree with the Prime Minister that our relationship with the US is absolutely critical and I think that everybody will accept that the President should pay a visit to the UK.
“The point about a state visit is that it directly involves the Queen in a very personal way.
“It’s the Queen’s invitation and the fact that the invitation was given within the first days of President Trump arriving in the White House, apparently to happen in the first few months of his presidency, means that it comes much faster than it has to previous US presidents.”
Ricketts said that Barack Obama, George W. Bush and Bill Clinton did not receive such a visit until well into their terms of office.
He added: “My concern is that the Queen would have acted on government advice, as she always does, clearly now there is a lot of controversy around that and if that continues then it seems to me that it does put the Queen in a difficult position.
“She would want to receive the president in a celebratory, warm, friendly visit... at the moment it looks quite controversial.”
Ricketts described the current political climate as “turbulent”, citing the controversial policies Trump has made in less than two weeks in office.
While agreeing that the offer cannot be withdrawn, Ricketts suggested the timing of the visit be pushed back.
“If the current level of opposition and protest goes on then I do think the Queen is put in a difficult position.”
In a letter to The Times, Lord Ricketts had described the offer as being “premature”.
“It would have been far wiser to wait to see what sort of president he would turn out to be before advising the Queen to invite him,” he said.
The petition calling for Trump’s state visit to be cancelled is the second most popular government petition ever, with calls for a second European Union Referendum in first place.
A statement on the Trump petition reads: “Donald Trump should be allowed to enter the UK in his capacity as head of the US Government, but he should not be invited to make an official state visit because it would cause embarrassment to Her Majesty the Queen.”
It continues: “Donald Trump’s well documented misogyny and vulgarity disqualifies him from being received by Her Majesty the Queen or the Prince of Wales.
“Therefore during the term of his presidency Donald Trump should not be invited to the United Kingdom for an official State Visit.”